@font-face {
  font-family: 'KaTeX_AMS';
  src: url('fonts/KaTeX_AMS-Regular.eot');
  src: url('fonts/KaTeX_AMS-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_AMS-Regular.woff2') format('woff2'), url('fonts/KaTeX_AMS-Regular.woff') format('woff'), url('fonts/KaTeX_AMS-Regular.ttf') format('truetype');
  font-weight: normal;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Caligraphic';
  src: url('fonts/KaTeX_Caligraphic-Bold.eot');
  src: url('fonts/KaTeX_Caligraphic-Bold.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Caligraphic-Bold.woff2') format('woff2'), url('fonts/KaTeX_Caligraphic-Bold.woff') format('woff'), url('fonts/KaTeX_Caligraphic-Bold.ttf') format('truetype');
  font-weight: bold;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Caligraphic';
  src: url('fonts/KaTeX_Caligraphic-Regular.eot');
  src: url('fonts/KaTeX_Caligraphic-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Caligraphic-Regular.woff2') format('woff2'), url('fonts/KaTeX_Caligraphic-Regular.woff') format('woff'), url('fonts/KaTeX_Caligraphic-Regular.ttf') format('truetype');
  font-weight: normal;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Fraktur';
  src: url('fonts/KaTeX_Fraktur-Bold.eot');
  src: url('fonts/KaTeX_Fraktur-Bold.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Fraktur-Bold.woff2') format('woff2'), url('fonts/KaTeX_Fraktur-Bold.woff') format('woff'), url('fonts/KaTeX_Fraktur-Bold.ttf') format('truetype');
  font-weight: bold;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Fraktur';
  src: url('fonts/KaTeX_Fraktur-Regular.eot');
  src: url('fonts/KaTeX_Fraktur-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Fraktur-Regular.woff2') format('woff2'), url('fonts/KaTeX_Fraktur-Regular.woff') format('woff'), url('fonts/KaTeX_Fraktur-Regular.ttf') format('truetype');
  font-weight: normal;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Main';
  src: url('fonts/KaTeX_Main-Bold.eot');
  src: url('fonts/KaTeX_Main-Bold.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Main-Bold.woff2') format('woff2'), url('fonts/KaTeX_Main-Bold.woff') format('woff'), url('fonts/KaTeX_Main-Bold.ttf') format('truetype');
  font-weight: bold;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Main';
  src: url('fonts/KaTeX_Main-Italic.eot');
  src: url('fonts/KaTeX_Main-Italic.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Main-Italic.woff2') format('woff2'), url('fonts/KaTeX_Main-Italic.woff') format('woff'), url('fonts/KaTeX_Main-Italic.ttf') format('truetype');
  font-weight: normal;
  font-style: italic;
}
@font-face {
  font-family: 'KaTeX_Main';
  src: url('fonts/KaTeX_Main-Regular.eot');
  src: url('fonts/KaTeX_Main-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Main-Regular.woff2') format('woff2'), url('fonts/KaTeX_Main-Regular.woff') format('woff'), url('fonts/KaTeX_Main-Regular.ttf') format('truetype');
  font-weight: normal;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Math';
  src: url('fonts/KaTeX_Math-Italic.eot');
  src: url('fonts/KaTeX_Math-Italic.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Math-Italic.woff2') format('woff2'), url('fonts/KaTeX_Math-Italic.woff') format('woff'), url('fonts/KaTeX_Math-Italic.ttf') format('truetype');
  font-weight: normal;
  font-style: italic;
}
@font-face {
  font-family: 'KaTeX_SansSerif';
  src: url('fonts/KaTeX_SansSerif-Regular.eot');
  src: url('fonts/KaTeX_SansSerif-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_SansSerif-Regular.woff2') format('woff2'), url('fonts/KaTeX_SansSerif-Regular.woff') format('woff'), url('fonts/KaTeX_SansSerif-Regular.ttf') format('truetype');
  font-weight: normal;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Script';
  src: url('fonts/KaTeX_Script-Regular.eot');
  src: url('fonts/KaTeX_Script-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Script-Regular.woff2') format('woff2'), url('fonts/KaTeX_Script-Regular.woff') format('woff'), url('fonts/KaTeX_Script-Regular.ttf') format('truetype');
  font-weight: normal;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Size1';
  src: url('fonts/KaTeX_Size1-Regular.eot');
  src: url('fonts/KaTeX_Size1-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size1-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size1-Regular.woff') format('woff'), url('fonts/KaTeX_Size1-Regular.ttf') format('truetype');
  font-weight: normal;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Size2';
  src: url('fonts/KaTeX_Size2-Regular.eot');
  src: url('fonts/KaTeX_Size2-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size2-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size2-Regular.woff') format('woff'), url('fonts/KaTeX_Size2-Regular.ttf') format('truetype');
  font-weight: normal;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Size3';
  src: url('fonts/KaTeX_Size3-Regular.eot');
  src: url('fonts/KaTeX_Size3-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size3-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size3-Regular.woff') format('woff'), url('fonts/KaTeX_Size3-Regular.ttf') format('truetype');
  font-weight: normal;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Size4';
  src: url('fonts/KaTeX_Size4-Regular.eot');
  src: url('fonts/KaTeX_Size4-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Size4-Regular.woff2') format('woff2'), url('fonts/KaTeX_Size4-Regular.woff') format('woff'), url('fonts/KaTeX_Size4-Regular.ttf') format('truetype');
  font-weight: normal;
  font-style: normal;
}
@font-face {
  font-family: 'KaTeX_Typewriter';
  src: url('fonts/KaTeX_Typewriter-Regular.eot');
  src: url('fonts/KaTeX_Typewriter-Regular.eot#iefix') format('embedded-opentype'), url('fonts/KaTeX_Typewriter-Regular.woff2') format('woff2'), url('fonts/KaTeX_Typewriter-Regular.woff') format('woff'), url('fonts/KaTeX_Typewriter-Regular.ttf') format('truetype');
  font-weight: normal;
  font-style: normal;
}
.katex-display {
  display: block;
  margin: 1em 0;
  text-align: center;
}
.katex-display > .katex {
  display: inline-block;
  text-align: initial;
}
.katex {
  font: normal 1.21em KaTeX_Main, Times New Roman, serif;
  line-height: 1.2;
  white-space: nowrap;
  text-indent: 0;
  text-rendering: auto;
}
.katex * {
  -ms-high-contrast-adjust: none !important;
}
.katex .katex-html {
  display: inline-block;
}
.katex .katex-mathml {
  position: absolute;
  clip: rect(1px, 1px, 1px, 1px);
  padding: 0;
  border: 0;
  height: 1px;
  width: 1px;
  overflow: hidden;
}
.katex .base {
  position: relative;
  display: inline-block;
}
.katex .strut {
  display: inline-block;
}
.katex .mathrm {
  font-style: normal;
}
.katex .textit {
  font-style: italic;
}
.katex .mathit {
  font-family: KaTeX_Math;
  font-style: italic;
}
.katex .mathbf {
  font-family: KaTeX_Main;
  font-weight: bold;
}
.katex .amsrm {
  font-family: KaTeX_AMS;
}
.katex .mathbb {
  font-family: KaTeX_AMS;
}
.katex .mathcal {
  font-family: KaTeX_Caligraphic;
}
.katex .mathfrak {
  font-family: KaTeX_Fraktur;
}
.katex .mathtt {
  font-family: KaTeX_Typewriter;
}
.katex .mathscr {
  font-family: KaTeX_Script;
}
.katex .mathsf {
  font-family: KaTeX_SansSerif;
}
.katex .mainit {
  font-family: KaTeX_Main;
  font-style: italic;
}
.katex .mainrm {
  font-family: KaTeX_Main;
  font-style: normal;
}
.katex .mord + .mop {
  margin-left: 0.16667em;
}
.katex .mord + .mbin {
  margin-left: 0.22222em;
}
.katex .mord + .mrel {
  margin-left: 0.27778em;
}
.katex .mord + .minner {
  margin-left: 0.16667em;
}
.katex .mop + .mord {
  margin-left: 0.16667em;
}
.katex .mop + .mop {
  margin-left: 0.16667em;
}
.katex .mop + .mrel {
  margin-left: 0.27778em;
}
.katex .mop + .minner {
  margin-left: 0.16667em;
}
.katex .mbin + .mord {
  margin-left: 0.22222em;
}
.katex .mbin + .mop {
  margin-left: 0.22222em;
}
.katex .mbin + .mopen {
  margin-left: 0.22222em;
}
.katex .mbin + .minner {
  margin-left: 0.22222em;
}
.katex .mrel + .mord {
  margin-left: 0.27778em;
}
.katex .mrel + .mop {
  margin-left: 0.27778em;
}
.katex .mrel + .mopen {
  margin-left: 0.27778em;
}
.katex .mrel + .minner {
  margin-left: 0.27778em;
}
.katex .mclose + .mop {
  margin-left: 0.16667em;
}
.katex .mclose + .mbin {
  margin-left: 0.22222em;
}
.katex .mclose + .mrel {
  margin-left: 0.27778em;
}
.katex .mclose + .minner {
  margin-left: 0.16667em;
}
.katex .mpunct + .mord {
  margin-left: 0.16667em;
}
.katex .mpunct + .mop {
  margin-left: 0.16667em;
}
.katex .mpunct + .mrel {
  margin-left: 0.16667em;
}
.katex .mpunct + .mopen {
  margin-left: 0.16667em;
}
.katex .mpunct + .mclose {
  margin-left: 0.16667em;
}
.katex .mpunct + .mpunct {
  margin-left: 0.16667em;
}
.katex .mpunct + .minner {
  margin-left: 0.16667em;
}
.katex .minner + .mord {
  margin-left: 0.16667em;
}
.katex .minner + .mop {
  margin-left: 0.16667em;
}
.katex .minner + .mbin {
  margin-left: 0.22222em;
}
.katex .minner + .mrel {
  margin-left: 0.27778em;
}
.katex .minner + .mopen {
  margin-left: 0.16667em;
}
.katex .minner + .mpunct {
  margin-left: 0.16667em;
}
.katex .minner + .minner {
  margin-left: 0.16667em;
}
.katex .mord.mtight {
  margin-left: 0;
}
.katex .mop.mtight {
  margin-left: 0;
}
.katex .mbin.mtight {
  margin-left: 0;
}
.katex .mrel.mtight {
  margin-left: 0;
}
.katex .mopen.mtight {
  margin-left: 0;
}
.katex .mclose.mtight {
  margin-left: 0;
}
.katex .mpunct.mtight {
  margin-left: 0;
}
.katex .minner.mtight {
  margin-left: 0;
}
.katex .mord + .mop.mtight {
  margin-left: 0.16667em;
}
.katex .mop + .mord.mtight {
  margin-left: 0.16667em;
}
.katex .mop + .mop.mtight {
  margin-left: 0.16667em;
}
.katex .mclose + .mop.mtight {
  margin-left: 0.16667em;
}
.katex .minner + .mop.mtight {
  margin-left: 0.16667em;
}
.katex .vlist-t {
  display: inline-table;
  table-layout: fixed;
}
.katex .vlist-r {
  display: table-row;
}
.katex .vlist {
  display: table-cell;
  vertical-align: bottom;
  position: relative;
}
.katex .vlist > span {
  display: block;
  height: 0;
  position: relative;
}
.katex .vlist > span > span {
  display: inline-block;
}
.katex .vlist > span > .pstrut {
  overflow: hidden;
  width: 0;
}
.katex .vlist-t2 {
  margin-right: -2px;
}
.katex .vlist-s {
  display: table-cell;
  vertical-align: bottom;
  font-size: 1px;
  width: 2px;
}
.katex .msupsub {
  text-align: left;
}
.katex .mfrac > span > span {
  text-align: center;
}
.katex .mfrac .frac-line {
  display: inline-block;
  width: 100%;
  border-bottom-style: solid;
}
.katex .mspace {
  display: inline-block;
}
.katex .mspace.negativethinspace {
  margin-left: -0.16667em;
}
.katex .mspace.thinspace {
  width: 0.16667em;
}
.katex .mspace.negativemediumspace {
  margin-left: -0.22222em;
}
.katex .mspace.mediumspace {
  width: 0.22222em;
}
.katex .mspace.thickspace {
  width: 0.27778em;
}
.katex .mspace.sixmuspace {
  width: 0.333333em;
}
.katex .mspace.eightmuspace {
  width: 0.444444em;
}
.katex .mspace.enspace {
  width: 0.5em;
}
.katex .mspace.twelvemuspace {
  width: 0.666667em;
}
.katex .mspace.quad {
  width: 1em;
}
.katex .mspace.qquad {
  width: 2em;
}
.katex .llap,
.katex .rlap {
  width: 0;
  position: relative;
}
.katex .llap > .inner,
.katex .rlap > .inner {
  position: absolute;
}
.katex .llap > .fix,
.katex .rlap > .fix {
  display: inline-block;
}
.katex .llap > .inner {
  right: 0;
}
.katex .rlap > .inner {
  left: 0;
}
.katex .katex-logo .a {
  font-size: 0.75em;
  margin-left: -0.32em;
  position: relative;
  top: -0.2em;
}
.katex .katex-logo .t {
  margin-left: -0.23em;
}
.katex .katex-logo .e {
  margin-left: -0.1667em;
  position: relative;
  top: 0.2155em;
}
.katex .katex-logo .x {
  margin-left: -0.125em;
}
.katex .rule {
  display: inline-block;
  border: solid 0;
  position: relative;
}
.katex .overline .overline-line,
.katex .underline .underline-line {
  display: inline-block;
  width: 100%;
  border-bottom-style: solid;
}
.katex .sqrt > .root {
  margin-left: 0.27777778em;
  margin-right: -0.55555556em;
}
.katex .sizing,
.katex .fontsize-ensurer {
  display: inline-block;
}
.katex .sizing.reset-size1.size1,
.katex .fontsize-ensurer.reset-size1.size1 {
  font-size: 1em;
}
.katex .sizing.reset-size1.size2,
.katex .fontsize-ensurer.reset-size1.size2 {
  font-size: 1.2em;
}
.katex .sizing.reset-size1.size3,
.katex .fontsize-ensurer.reset-size1.size3 {
  font-size: 1.4em;
}
.katex .sizing.reset-size1.size4,
.katex .fontsize-ensurer.reset-size1.size4 {
  font-size: 1.6em;
}
.katex .sizing.reset-size1.size5,
.katex .fontsize-ensurer.reset-size1.size5 {
  font-size: 1.8em;
}
.katex .sizing.reset-size1.size6,
.katex .fontsize-ensurer.reset-size1.size6 {
  font-size: 2em;
}
.katex .sizing.reset-size1.size7,
.katex .fontsize-ensurer.reset-size1.size7 {
  font-size: 2.4em;
}
.katex .sizing.reset-size1.size8,
.katex .fontsize-ensurer.reset-size1.size8 {
  font-size: 2.88em;
}
.katex .sizing.reset-size1.size9,
.katex .fontsize-ensurer.reset-size1.size9 {
  font-size: 3.456em;
}
.katex .sizing.reset-size1.size10,
.katex .fontsize-ensurer.reset-size1.size10 {
  font-size: 4.148em;
}
.katex .sizing.reset-size1.size11,
.katex .fontsize-ensurer.reset-size1.size11 {
  font-size: 4.976em;
}
.katex .sizing.reset-size2.size1,
.katex .fontsize-ensurer.reset-size2.size1 {
  font-size: 0.83333333em;
}
.katex .sizing.reset-size2.size2,
.katex .fontsize-ensurer.reset-size2.size2 {
  font-size: 1em;
}
.katex .sizing.reset-size2.size3,
.katex .fontsize-ensurer.reset-size2.size3 {
  font-size: 1.16666667em;
}
.katex .sizing.reset-size2.size4,
.katex .fontsize-ensurer.reset-size2.size4 {
  font-size: 1.33333333em;
}
.katex .sizing.reset-size2.size5,
.katex .fontsize-ensurer.reset-size2.size5 {
  font-size: 1.5em;
}
.katex .sizing.reset-size2.size6,
.katex .fontsize-ensurer.reset-size2.size6 {
  font-size: 1.66666667em;
}
.katex .sizing.reset-size2.size7,
.katex .fontsize-ensurer.reset-size2.size7 {
  font-size: 2em;
}
.katex .sizing.reset-size2.size8,
.katex .fontsize-ensurer.reset-size2.size8 {
  font-size: 2.4em;
}
.katex .sizing.reset-size2.size9,
.katex .fontsize-ensurer.reset-size2.size9 {
  font-size: 2.88em;
}
.katex .sizing.reset-size2.size10,
.katex .fontsize-ensurer.reset-size2.size10 {
  font-size: 3.45666667em;
}
.katex .sizing.reset-size2.size11,
.katex .fontsize-ensurer.reset-size2.size11 {
  font-size: 4.14666667em;
}
.katex .sizing.reset-size3.size1,
.katex .fontsize-ensurer.reset-size3.size1 {
  font-size: 0.71428571em;
}
.katex .sizing.reset-size3.size2,
.katex .fontsize-ensurer.reset-size3.size2 {
  font-size: 0.85714286em;
}
.katex .sizing.reset-size3.size3,
.katex .fontsize-ensurer.reset-size3.size3 {
  font-size: 1em;
}
.katex .sizing.reset-size3.size4,
.katex .fontsize-ensurer.reset-size3.size4 {
  font-size: 1.14285714em;
}
.katex .sizing.reset-size3.size5,
.katex .fontsize-ensurer.reset-size3.size5 {
  font-size: 1.28571429em;
}
.katex .sizing.reset-size3.size6,
.katex .fontsize-ensurer.reset-size3.size6 {
  font-size: 1.42857143em;
}
.katex .sizing.reset-size3.size7,
.katex .fontsize-ensurer.reset-size3.size7 {
  font-size: 1.71428571em;
}
.katex .sizing.reset-size3.size8,
.katex .fontsize-ensurer.reset-size3.size8 {
  font-size: 2.05714286em;
}
.katex .sizing.reset-size3.size9,
.katex .fontsize-ensurer.reset-size3.size9 {
  font-size: 2.46857143em;
}
.katex .sizing.reset-size3.size10,
.katex .fontsize-ensurer.reset-size3.size10 {
  font-size: 2.96285714em;
}
.katex .sizing.reset-size3.size11,
.katex .fontsize-ensurer.reset-size3.size11 {
  font-size: 3.55428571em;
}
.katex .sizing.reset-size4.size1,
.katex .fontsize-ensurer.reset-size4.size1 {
  font-size: 0.625em;
}
.katex .sizing.reset-size4.size2,
.katex .fontsize-ensurer.reset-size4.size2 {
  font-size: 0.75em;
}
.katex .sizing.reset-size4.size3,
.katex .fontsize-ensurer.reset-size4.size3 {
  font-size: 0.875em;
}
.katex .sizing.reset-size4.size4,
.katex .fontsize-ensurer.reset-size4.size4 {
  font-size: 1em;
}
.katex .sizing.reset-size4.size5,
.katex .fontsize-ensurer.reset-size4.size5 {
  font-size: 1.125em;
}
.katex .sizing.reset-size4.size6,
.katex .fontsize-ensurer.reset-size4.size6 {
  font-size: 1.25em;
}
.katex .sizing.reset-size4.size7,
.katex .fontsize-ensurer.reset-size4.size7 {
  font-size: 1.5em;
}
.katex .sizing.reset-size4.size8,
.katex .fontsize-ensurer.reset-size4.size8 {
  font-size: 1.8em;
}
.katex .sizing.reset-size4.size9,
.katex .fontsize-ensurer.reset-size4.size9 {
  font-size: 2.16em;
}
.katex .sizing.reset-size4.size10,
.katex .fontsize-ensurer.reset-size4.size10 {
  font-size: 2.5925em;
}
.katex .sizing.reset-size4.size11,
.katex .fontsize-ensurer.reset-size4.size11 {
  font-size: 3.11em;
}
.katex .sizing.reset-size5.size1,
.katex .fontsize-ensurer.reset-size5.size1 {
  font-size: 0.55555556em;
}
.katex .sizing.reset-size5.size2,
.katex .fontsize-ensurer.reset-size5.size2 {
  font-size: 0.66666667em;
}
.katex .sizing.reset-size5.size3,
.katex .fontsize-ensurer.reset-size5.size3 {
  font-size: 0.77777778em;
}
.katex .sizing.reset-size5.size4,
.katex .fontsize-ensurer.reset-size5.size4 {
  font-size: 0.88888889em;
}
.katex .sizing.reset-size5.size5,
.katex .fontsize-ensurer.reset-size5.size5 {
  font-size: 1em;
}
.katex .sizing.reset-size5.size6,
.katex .fontsize-ensurer.reset-size5.size6 {
  font-size: 1.11111111em;
}
.katex .sizing.reset-size5.size7,
.katex .fontsize-ensurer.reset-size5.size7 {
  font-size: 1.33333333em;
}
.katex .sizing.reset-size5.size8,
.katex .fontsize-ensurer.reset-size5.size8 {
  font-size: 1.6em;
}
.katex .sizing.reset-size5.size9,
.katex .fontsize-ensurer.reset-size5.size9 {
  font-size: 1.92em;
}
.katex .sizing.reset-size5.size10,
.katex .fontsize-ensurer.reset-size5.size10 {
  font-size: 2.30444444em;
}
.katex .sizing.reset-size5.size11,
.katex .fontsize-ensurer.reset-size5.size11 {
  font-size: 2.76444444em;
}
.katex .sizing.reset-size6.size1,
.katex .fontsize-ensurer.reset-size6.size1 {
  font-size: 0.5em;
}
.katex .sizing.reset-size6.size2,
.katex .fontsize-ensurer.reset-size6.size2 {
  font-size: 0.6em;
}
.katex .sizing.reset-size6.size3,
.katex .fontsize-ensurer.reset-size6.size3 {
  font-size: 0.7em;
}
.katex .sizing.reset-size6.size4,
.katex .fontsize-ensurer.reset-size6.size4 {
  font-size: 0.8em;
}
.katex .sizing.reset-size6.size5,
.katex .fontsize-ensurer.reset-size6.size5 {
  font-size: 0.9em;
}
.katex .sizing.reset-size6.size6,
.katex .fontsize-ensurer.reset-size6.size6 {
  font-size: 1em;
}
.katex .sizing.reset-size6.size7,
.katex .fontsize-ensurer.reset-size6.size7 {
  font-size: 1.2em;
}
.katex .sizing.reset-size6.size8,
.katex .fontsize-ensurer.reset-size6.size8 {
  font-size: 1.44em;
}
.katex .sizing.reset-size6.size9,
.katex .fontsize-ensurer.reset-size6.size9 {
  font-size: 1.728em;
}
.katex .sizing.reset-size6.size10,
.katex .fontsize-ensurer.reset-size6.size10 {
  font-size: 2.074em;
}
.katex .sizing.reset-size6.size11,
.katex .fontsize-ensurer.reset-size6.size11 {
  font-size: 2.488em;
}
.katex .sizing.reset-size7.size1,
.katex .fontsize-ensurer.reset-size7.size1 {
  font-size: 0.41666667em;
}
.katex .sizing.reset-size7.size2,
.katex .fontsize-ensurer.reset-size7.size2 {
  font-size: 0.5em;
}
.katex .sizing.reset-size7.size3,
.katex .fontsize-ensurer.reset-size7.size3 {
  font-size: 0.58333333em;
}
.katex .sizing.reset-size7.size4,
.katex .fontsize-ensurer.reset-size7.size4 {
  font-size: 0.66666667em;
}
.katex .sizing.reset-size7.size5,
.katex .fontsize-ensurer.reset-size7.size5 {
  font-size: 0.75em;
}
.katex .sizing.reset-size7.size6,
.katex .fontsize-ensurer.reset-size7.size6 {
  font-size: 0.83333333em;
}
.katex .sizing.reset-size7.size7,
.katex .fontsize-ensurer.reset-size7.size7 {
  font-size: 1em;
}
.katex .sizing.reset-size7.size8,
.katex .fontsize-ensurer.reset-size7.size8 {
  font-size: 1.2em;
}
.katex .sizing.reset-size7.size9,
.katex .fontsize-ensurer.reset-size7.size9 {
  font-size: 1.44em;
}
.katex .sizing.reset-size7.size10,
.katex .fontsize-ensurer.reset-size7.size10 {
  font-size: 1.72833333em;
}
.katex .sizing.reset-size7.size11,
.katex .fontsize-ensurer.reset-size7.size11 {
  font-size: 2.07333333em;
}
.katex .sizing.reset-size8.size1,
.katex .fontsize-ensurer.reset-size8.size1 {
  font-size: 0.34722222em;
}
.katex .sizing.reset-size8.size2,
.katex .fontsize-ensurer.reset-size8.size2 {
  font-size: 0.41666667em;
}
.katex .sizing.reset-size8.size3,
.katex .fontsize-ensurer.reset-size8.size3 {
  font-size: 0.48611111em;
}
.katex .sizing.reset-size8.size4,
.katex .fontsize-ensurer.reset-size8.size4 {
  font-size: 0.55555556em;
}
.katex .sizing.reset-size8.size5,
.katex .fontsize-ensurer.reset-size8.size5 {
  font-size: 0.625em;
}
.katex .sizing.reset-size8.size6,
.katex .fontsize-ensurer.reset-size8.size6 {
  font-size: 0.69444444em;
}
.katex .sizing.reset-size8.size7,
.katex .fontsize-ensurer.reset-size8.size7 {
  font-size: 0.83333333em;
}
.katex .sizing.reset-size8.size8,
.katex .fontsize-ensurer.reset-size8.size8 {
  font-size: 1em;
}
.katex .sizing.reset-size8.size9,
.katex .fontsize-ensurer.reset-size8.size9 {
  font-size: 1.2em;
}
.katex .sizing.reset-size8.size10,
.katex .fontsize-ensurer.reset-size8.size10 {
  font-size: 1.44027778em;
}
.katex .sizing.reset-size8.size11,
.katex .fontsize-ensurer.reset-size8.size11 {
  font-size: 1.72777778em;
}
.katex .sizing.reset-size9.size1,
.katex .fontsize-ensurer.reset-size9.size1 {
  font-size: 0.28935185em;
}
.katex .sizing.reset-size9.size2,
.katex .fontsize-ensurer.reset-size9.size2 {
  font-size: 0.34722222em;
}
.katex .sizing.reset-size9.size3,
.katex .fontsize-ensurer.reset-size9.size3 {
  font-size: 0.40509259em;
}
.katex .sizing.reset-size9.size4,
.katex .fontsize-ensurer.reset-size9.size4 {
  font-size: 0.46296296em;
}
.katex .sizing.reset-size9.size5,
.katex .fontsize-ensurer.reset-size9.size5 {
  font-size: 0.52083333em;
}
.katex .sizing.reset-size9.size6,
.katex .fontsize-ensurer.reset-size9.size6 {
  font-size: 0.5787037em;
}
.katex .sizing.reset-size9.size7,
.katex .fontsize-ensurer.reset-size9.size7 {
  font-size: 0.69444444em;
}
.katex .sizing.reset-size9.size8,
.katex .fontsize-ensurer.reset-size9.size8 {
  font-size: 0.83333333em;
}
.katex .sizing.reset-size9.size9,
.katex .fontsize-ensurer.reset-size9.size9 {
  font-size: 1em;
}
.katex .sizing.reset-size9.size10,
.katex .fontsize-ensurer.reset-size9.size10 {
  font-size: 1.20023148em;
}
.katex .sizing.reset-size9.size11,
.katex .fontsize-ensurer.reset-size9.size11 {
  font-size: 1.43981481em;
}
.katex .sizing.reset-size10.size1,
.katex .fontsize-ensurer.reset-size10.size1 {
  font-size: 0.24108004em;
}
.katex .sizing.reset-size10.size2,
.katex .fontsize-ensurer.reset-size10.size2 {
  font-size: 0.28929605em;
}
.katex .sizing.reset-size10.size3,
.katex .fontsize-ensurer.reset-size10.size3 {
  font-size: 0.33751205em;
}
.katex .sizing.reset-size10.size4,
.katex .fontsize-ensurer.reset-size10.size4 {
  font-size: 0.38572806em;
}
.katex .sizing.reset-size10.size5,
.katex .fontsize-ensurer.reset-size10.size5 {
  font-size: 0.43394407em;
}
.katex .sizing.reset-size10.size6,
.katex .fontsize-ensurer.reset-size10.size6 {
  font-size: 0.48216008em;
}
.katex .sizing.reset-size10.size7,
.katex .fontsize-ensurer.reset-size10.size7 {
  font-size: 0.57859209em;
}
.katex .sizing.reset-size10.size8,
.katex .fontsize-ensurer.reset-size10.size8 {
  font-size: 0.69431051em;
}
.katex .sizing.reset-size10.size9,
.katex .fontsize-ensurer.reset-size10.size9 {
  font-size: 0.83317261em;
}
.katex .sizing.reset-size10.size10,
.katex .fontsize-ensurer.reset-size10.size10 {
  font-size: 1em;
}
.katex .sizing.reset-size10.size11,
.katex .fontsize-ensurer.reset-size10.size11 {
  font-size: 1.19961427em;
}
.katex .sizing.reset-size11.size1,
.katex .fontsize-ensurer.reset-size11.size1 {
  font-size: 0.20096463em;
}
.katex .sizing.reset-size11.size2,
.katex .fontsize-ensurer.reset-size11.size2 {
  font-size: 0.24115756em;
}
.katex .sizing.reset-size11.size3,
.katex .fontsize-ensurer.reset-size11.size3 {
  font-size: 0.28135048em;
}
.katex .sizing.reset-size11.size4,
.katex .fontsize-ensurer.reset-size11.size4 {
  font-size: 0.32154341em;
}
.katex .sizing.reset-size11.size5,
.katex .fontsize-ensurer.reset-size11.size5 {
  font-size: 0.36173633em;
}
.katex .sizing.reset-size11.size6,
.katex .fontsize-ensurer.reset-size11.size6 {
  font-size: 0.40192926em;
}
.katex .sizing.reset-size11.size7,
.katex .fontsize-ensurer.reset-size11.size7 {
  font-size: 0.48231511em;
}
.katex .sizing.reset-size11.size8,
.katex .fontsize-ensurer.reset-size11.size8 {
  font-size: 0.57877814em;
}
.katex .sizing.reset-size11.size9,
.katex .fontsize-ensurer.reset-size11.size9 {
  font-size: 0.69453376em;
}
.katex .sizing.reset-size11.size10,
.katex .fontsize-ensurer.reset-size11.size10 {
  font-size: 0.83360129em;
}
.katex .sizing.reset-size11.size11,
.katex .fontsize-ensurer.reset-size11.size11 {
  font-size: 1em;
}
.katex .delimsizing.size1 {
  font-family: KaTeX_Size1;
}
.katex .delimsizing.size2 {
  font-family: KaTeX_Size2;
}
.katex .delimsizing.size3 {
  font-family: KaTeX_Size3;
}
.katex .delimsizing.size4 {
  font-family: KaTeX_Size4;
}
.katex .delimsizing.mult .delim-size1 > span {
  font-family: KaTeX_Size1;
}
.katex .delimsizing.mult .delim-size4 > span {
  font-family: KaTeX_Size4;
}
.katex .nulldelimiter {
  display: inline-block;
  width: 0.12em;
}
.katex .delimcenter {
  position: relative;
}
.katex .op-symbol {
  position: relative;
}
.katex .op-symbol.small-op {
  font-family: KaTeX_Size1;
}
.katex .op-symbol.large-op {
  font-family: KaTeX_Size2;
}
.katex .op-limits > .vlist-t {
  text-align: center;
}
.katex .accent > .vlist-t {
  text-align: center;
}
.katex .accent .accent-body > span {
  width: 0;
}
.katex .accent .accent-body.accent-vec > span {
  position: relative;
  left: 0.326em;
}
.katex .accent .accent-body.accent-hungarian > span {
  position: relative;
  left: 0.250em;
}
.katex .mtable .vertical-separator {
  display: inline-block;
  margin: 0 -0.025em;
  border-right: 0.05em solid black;
}
.katex .mtable .arraycolsep {
  display: inline-block;
}
.katex .mtable .col-align-c > .vlist-t {
  text-align: center;
}
.katex .mtable .col-align-l > .vlist-t {
  text-align: left;
}
.katex .mtable .col-align-r > .vlist-t {
  text-align: right;
}
.katex .svg-align {
  text-align: left;
}
.katex svg {
  display: block;
  position: absolute;
  width: 100%;
}
.katex svg path {
  fill: currentColor;
}
.katex svg line {
  stroke: currentColor;
}
.katex .stretchy {
  width: 100%;
  display: block;
}
.katex .stretchy:before,
.katex .stretchy:after {
  content: "";
}
.katex .x-arrow-pad {
  padding: 0 0.5em;
}
.katex .x-arrow,
.katex .mover,
.katex .munder {
  text-align: center;
}
.katex .boxpad {
  padding: 0 0.3em 0 0.3em;
}
.katex .fbox {
  box-sizing: border-box;
  border: 0.04em solid black;
}
.katex .cancel-pad {
  padding: 0 0.2em 0 0.2em;
}
.katex .mord + .cancel-lap,
.katex .mbin + .cancel-lap {
  margin-left: -0.2em;
}
.katex .cancel-lap + .mord,
.katex .cancel-lap + .mbin,
.katex .cancel-lap + .msupsub {
  margin-left: -0.2em;
}
.katex .sout {
  border-bottom-style: solid;
  border-bottom-width: 0.08em;
}
